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This article investigates an aggregative game based on Euler-Lagrange systems subject to time-varying communication delays. First, a distributed algorithm is put forward to try to find the Nash equilibrium by the deliberated group of Euler-Lagrange systems with “small” delay and “large” delay. Second, we illustrate the convergence of two circumstances, separately. The first circumstance derives the upper bound of delays for guaranteeing globally exponential convergence, and the other obtains globally exponential convergence, even in some restrictions on “large” delays. Finally, a numerical example is used to show the effectiveness and superiority of proposed method.